The kinetic energy of a freely cooling granular gas decreases as a power law t −θ at large times t. Two theoretical conjectures exist for the exponent θ. One based on ballistic aggregation of compact spherical aggregates predicts θ = 2d/(d + 2) in d dimensions. The other based on Burgers equation describing anisotropic, extended clusters predicts θ = d/2 when 2 ≤ d ≤ 4. We do extensive simulations in three dimensions to find that while θ is as predicted by ballistic aggregation, the cluster statistics and velocity distribution differ from it. Thus, the freely cooling granular gas fits to neither the ballistic aggregation or a Burgers equation description. The freely cooling granular gas, a collection of ballistically moving inelastic particles with no external source of energy, has been used to describe dynamics of granular materials [1][2][3], large scale structure formation in the universe [4] and geophysical flows [5]. It is also of interest as a system far from equilibrium, limiting cases being amenable to exact analysis [6,7], has close connection to the well studied Burgers equation [6,[8][9][10][11], and is an example of an ordering system showing non-trivial coarsening behavior [12][13][14][15]. Of primary interest is clustering of particles due to inelastic collisions and the temporal evolution of the kinetic energy E(t) at large times.At initial times, particles remain homogeneously distributed and kinetic theory predicts that E(t) decreases as (1 + t/t 0 ) −2 (Haff's law) where the time scale t 0 ∝ (1 − r 2 ) −1 for constant coefficient of restitution r [16]. At later times, this regime is destabilized by long wavelength fluctuations into an inhomogeneous cooling regime dominated by clustering of particles [17][18][19]. In this latter regime, E(t) no longer obeys Haff's law but decreases as a power law t −θ , where θ depends only on dimension d [20,21]. Direct experiments on inelastic particles under levitation [22] or in microgravity [23,24] confirm Haff's law. However, being limited by small number of particles and short times, they do not probe the inhomogeneous regime giving no information about θ.Different theories predict different values of θ. The extension of kinetic theory into the inhomogeneous cooling regime using mode coupling methods leads to E(τ ) ∼ τ −d/2 , where the relation between the average number of collisions per particle τ and time t is unclear [25]. This result agrees with simulations for near-elastic (r ≈ 1) gases, but fails for large times and strongly inelastic (r ≪ 1) gases [25]. Any theory involving perturbing about the elastic limit r = 1 is unlikely to succeed since extensive simulations in one [20] and two [21] dimensions show that for any r < 1, the system is akin to a sticky gas (r → 0), such that colliding particles stick and form aggregates.If it is assumed that the aggregates are compact spherical objects, then the sticky limit corresponds to the well studied ballistic aggregation model (BA) (see Ref.[26] for a review). For BA in the dilute limit and the mean field...

We study the inhomogeneous clustered regime of a freely cooling granular gas of rough particles in two dimensions using large-scale event-driven simulations and scaling arguments. During collisions, rough particles dissipate energy in both the normal and tangential directions of collision. In the inhomogeneous regime, translational kinetic energy and the rotational energy decay with time t as power laws t −θ T and t −θ R . We numerically determine θT ≈ 1 and θR ≈ 1.6, independent of the coefficients of restitution. The inhomogeneous regime of the granular gas has been argued to be describable by the ballistic aggregation problem, where particles coalesce on contact. Using scaling arguments, we predict θT = 1 and θR = 1 for ballistic aggregation, θR being different from that obtained for the rough granular gas. Simulations of ballistic aggregation with rotational degrees of freedom are consistent with these exponents.

The mechanical and transport properties of jammed materials originate from an underlying percolating network of contact forces between the grains. Using extensive simulations we investigate the force-percolation transition of this network, where two particles are considered as linked if their interparticle force overcomes a threshold. We show that this transition belongs to the random percolation universality class, thus ruling out the existence of long-range correlations between the forces. Through a combined size and pressure scaling for the percolative quantities, we show that the continuous force percolation transition evolves into the discontinuous jamming transition in the zero pressure limit, as the size of the critical region scales with the pressure.

We analyze a recent experiment [Boudet, Cassagne, and Kellay, Phys. Rev. Lett. 103, 224501 (2009)] in which the shock created by the impact of a steel ball on a flowing monolayer of glass beads is studied quantitatively. We argue that radial momentum is conserved in the process and hence show that in two dimensions the shock radius increases in time t as a power law t{1/3}. This is confirmed in event driven simulations of an inelastic hard sphere system. The experimental data are compared with the theoretical prediction and are shown to compare well at intermediate times. At long times the experimental data exhibit a crossover to a different scaling behavior. We attribute this to the problem becoming effectively three dimensional due to the accumulation of particles at the shock front and propose a simple hard sphere model that incorporates this effect. Simulations of this model capture the crossover seen in the experimental data.

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